Synchronous motors are more and more widely used due to their small volumes and high efficiencies. The electromagnetic torque T of a motor can be expressed in terms of co energy Wco as
  T  =                    ∂        Wco                    ∂        θ              |                  i        const            .      Self and mutual inductance coefficients of the armature are dependent on the rotor angular position θ, thus, the electromagnetic torque also can be expressed as
      T    =                            ∑                      i            =            1                    Z                ⁢                                  ⁢                              F            m                    ⁢                      i            i                    ⁢                                                    dM                im                            ⁡                              (                θ                )                                                    d              ⁢                                                          ⁢              θ                                          +                        1          2                ⁢                  F          m          2                ⁢                              dP            m                                d            ⁢                                                  ⁢            θ                                ,wherein Z is the number of phases, Fm is the equivalent magnetic motive force (MMF) of the magnets, Pm is the magnetic circuit permeance of the magnets, I is the stator winding current, Mim is the mutual inductance between a stator winding and the one turn equivalent circuit of the magnets. The electromotive force (EMF) of a stator winding ei is related to the magnet flux by
            e      i        =                  -                              d            ⁢                                                  ⁢                          ϕ              im                                dt                    =                        -                      ω            m                          ⁢                  F          m                ⁢                                            dM              im                        ⁡                          (              θ              )                                            d            ⁢                                                  ⁢            θ                                ,wherein ϕim is the magnetic flux produced by the magnets. From the above two formulas, the electromagnetic torque T can be obtained by
  T  =            -                        ∑                      i            =            1                    Z                ⁢                                  ⁢                                            e              i                        ⁢                          i              i                                            ω            m                                +                  1        2            ⁢              F        m        2            ⁢                                    dP            m                                d            ⁢                                                  ⁢            θ                          .            Therefore, the product of back electromotive force (Bemf) and motor current contributes to the motor output power. However, if the product of Bemf and motor current is less than 0, i.e. if Bemf and motor current are out of phase, as shown in FIG. 1, then negative torque (−T) will act against positive torque (+T), so the motor power efficiency is reduced.